visualisasi fungsi di dekati deret maclaurin di R

1.    Visualisasi fungsi eksponen yang di dekati deret Maclaurin

x = seq(-5,5,by=0.1)

plot (c(-10,10),c(-2,2), type="n", xlab="X", ylab="Eksponen", main="Aproksimasi untuk Fungsi Eksponen")

abline (h=0,col="red")

abline (v=0,col="black")

lines (x, exp(x), col="red")

lines (x, x, col="pink")

lines (x, 1+x,col="blue")

lines (x, 1+x+(x^2/factorial(2)),col="green")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3)),col="yellow")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4)),col="pink")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5)),col="black")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6)),col="steelblue")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7)),col="blueviolet")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8)),col="purple")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9)),col="brown")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10)),col="red")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11)),col="tomato4")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11))+(x^12/factorial(12)),col="violetred4")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11))+(x^12/factorial(12))+(x^13/factorial(13)),col="thistle4")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11))+(x^12/factorial(12))+(x^13/factorial(13))+(x^14/factorial(14)),col="skyblue2")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11))+(x^12/factorial(12))+(x^13/factorial(13))+(x^14/factorial(14))+(x^15/factorial(15)),col="tan")

lines (x, 1+x+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))+(x^5/factorial(5))+(x^6/factorial(6))+(x^7/factorial(7))+(x^8/factorial(8))+(x^9/factorial(9))+(x^10/factorial(10))+(x^11/factorial(11))+(x^12/factorial(12))+(x^13/factorial(13))+(x^14/factorial(14))+(x^15/factorial(15))+(x^16/factorial(16)),col="Blue")

Jadi berdasarkan hasil aproksimasi diatas diketahui bahwa fungsi eksponen dapat di aproksimasi oleh deret Maclourin pada orde ke 16

2.        Visualisasi fungsi cosinus yang di dekati deret Maclaurin

x = seq(-10,10,by=0.1)

plot (c(-10,10),c(-2,2), type="n", xlab="X", ylab="Cos", main="Aproksimasi untuk Fungsi Cos")

abline (h=0,col="blue")

abline (v=0,col="blue")

lines (x, cos(x), col="red")

lines (x, x, col="yellow")

lines (x, 1-(x^2/factorial(2)), col="yellow")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4)), col="black")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6)), col="red")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8)), col="blue")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10)), col="brown")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12)), col="pink")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14)), col="orange")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16)), col="maroon")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18)), col="skyblue3")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20)), col="thistle4")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20))-(x^22/factorial(22)), col="tomato4")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20))-(x^22/factorial(22))+(x^24/factorial(24)), col="violetred")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20))-(x^22/factorial(22))+(x^24/factorial(24))-(x^26/factorial(26)), col="steelblue")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20))-(x^22/factorial(22))+(x^24/factorial(24))-(x^26/factorial(26))+(x^28/factorial(28)), col="violet")

lines (x, 1-(x^2/factorial(2))+(x^4/factorial(4))-(x^6/factorial(6))+(x^8/factorial(8))-(x^10/factorial(10))+(x^12/factorial(12))-(x^14/factorial(14))+(x^16/factorial(16))-(x^18/factorial(18))+(x^20/factorial(20))-(x^22/factorial(22))+(x^24/factorial(24))-(x^26/factorial(26))+(x^28/factorial(28))-(x^30/factorial(30)), col="black")

Jadi berdasarkan hasil aproksimasi diatas diketahui bahwa fungsi cos dapat di aproksimasi oleh deret Maclourin pada orde ke 30

3.      Visualisasi fungsi lon yang di dekati deret Maclaurin

x = seq(-1,1,by=0.1)

plot (c(-10,10),c(-2,2), type="n", xlab="X", ylab="Lon", main="Aproksimasi untuk Fungsi Lon")

abline (h=0,col="red")

abline (v=0,col="red")

lines (x, log(x+1), col="blue")

lines (x, x, col="green")

lines (x, x-(x^2/2), col="orange")

lines (x, x-(x^2/2)+(x^3/3), col="violetred")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4), col="tomato")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5), col="black")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5)-(x^6/6), col="tomato4")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5)-(x^6/6)+(x^7/7), col="firebrick3")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5)-(x^6/6)+(x^7/7)-(x^8/8), col="pink")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5)-(x^6/6)+(x^7/7)-(x^8/8)+(x^9/9), col="blue")

lines (x, x-(x^2/2)+(x^3/3)-(x^4/4)+(x^5/5)-(x^6/6)+(x^7/7)-(x^8/8)+(x^9/9)-(x^10/10), col="black")

Jadi berdasarkan hasil aproksimasi diatas diketahui bahwa fungsi cos dapat di aproksimasi oleh deret Maclourin pada orde ke 10